METODE ELEMEN BATAS UNTUK MENYELESAIKAN MASALAH PERPINDAHAN DAN PENYEBARAN POLUTAN DALAM MEDIA ISOTROPIK TANAH DIMENSI DUA; ( BOUNDARY ELEMENT METHODS FOR CONDUCTION-CONVECTION POLLUTANT PROBLEM IN THE LAND OF THE TWO DIMENSIONAL ISOTROPIC MEDIA )

Pertiwi, Yastika U A, Imam Solekhudin

2015 | Skripsi | FMIPA

Boundary Element Method (BEM) is one of the numerical methods based on discretization to solve differential equations subject to some boundary conditions which is constructed. One particular form of BEM is Dual Reciprocity Boundary Element Method (DRBEM) which is a numerical method to solve the Helmholtz or modified Helmholtz equation in a region subject to some boundary conditions. To determine the solution of the Helmholtz equation, we first express solution in the form of a boundary integral equation. This integral equation is then reduced into a system of linear algebraic equation. To reduce the integral equation, boundary is discretized into a number of line segments or elements, and a number of interior collocation points is chosen. Solving the system of linear algebraic, numerical solutions at collocation points can be obtained. Using the solutions, a numerical solution at any point may be obtained. In the final project,a DRBEM is applied to solve a problem involving a spread of pollutant in an isotropic soil. The governing equation of this problem may be written in a modified Helmholtz equation. The DRBEM is then implemented using MATLAB codes. The results are used to compare solutions obtained using the DRBEM with the corresponding analytical solution.

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